A227083 Number of ways to write n as a + b/2 with a and b terms of the sequence A008407.

0, 0, 1, 0, 1, 1, 1, 1, 2, 2, 1, 3, 1, 2, 2, 3, 2, 3, 2, 3, 3, 3, 3, 4, 1, 4, 4, 2, 3, 5, 3, 4, 5, 4, 3, 7, 4, 4, 3, 6, 5, 5, 3, 6, 5, 6, 4, 6, 4, 6, 7, 5, 5, 7, 4, 6, 6, 7, 4, 7, 6, 5, 8, 5, 6, 9, 6, 5, 6, 7, 8, 8, 6, 7, 7, 9, 7, 7, 5, 9, 10, 6, 8, 9, 8, 10, 7, 8, 7, 11, 8, 7, 9, 9, 10, 10, 8, 9, 8, 13

Offset

1,9

Comments

Conjecture: We have a(n) > 0 for all n > 4.

For every k = 2, ..., 342, the value of A008407(k) has been determined by T. J. Engelsma. Since A008407(343)/2 > A008407(342)/2 = 2328/2 = 1164, if n <= 1166 can be written as A008407(j) + A008407(k)/2 with j > 1 and k > 1 then neither j nor k exceeds 342. Based on this we are able to compute a(n) for n = 1, ..., 1166.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..1166

A. V. Sutherland, Narrow admissible k-tuples: bounds on H(k), 2013.

T. Tao, Bounded gaps between primes, PolyMath Wiki Project, 2013.

Example

a(10) = 2 since 10 = 2 + 16/2 = 6 + 8/2;
a(11) = 1 since 11 = 8 + 6/2;
a(25) = 1 since 25 = 12 + 26/2.

Crossrefs

Cf. A008407.

Sequence in context: A320040 A072528 A368060 * A327571 A166363 A117470

Adjacent sequences: A227080 A227081 A227082 * A227084 A227085 A227086

Keyword

nonn

Author

Zhi-Wei Sun, Jun 30 2013

Status

approved